Importantly, Eq. (12) implies a different leading-order strain rate dependency of flow stress in the regime of low strain rates. Eq. (11), which has been used often in the literature, predicts that the strain rate increases linearly with the 'effective stress' \(\tau _{\rm eff}^{\beta } = \tau ^{\beta } - \alpha ^{\beta } \mu b \sqrt{\rho ^{\beta }}\) , provided that the resolved shear stress exceeds the friction-like 'Taylor stress' : \(\dot{\gamma } \propto \tau _{\rm eff}^{\beta }\)  if \(|\tau ^{\beta }| \ge \alpha ^{\beta } \mu b \sqrt{\rho ^{\beta }}\) . Eq. (12), on the other hand, predicts a nonlinear increase, \(\dot{\gamma } \propto (\tau _{\rm eff}^{\beta })^{1/\eta }\) , as has been reported in simulations, see e.g. Miguel et. al. [1]}.
